Holomorphic approximation of CR functions on tubular submanifolds of ℂ²

André Boivin; Roman Dwilewicz

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 11-18
  • ISSN: 0066-2216

Abstract

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The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².

How to cite

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André Boivin, and Roman Dwilewicz. "Holomorphic approximation of CR functions on tubular submanifolds of ℂ²." Annales Polonici Mathematici 55.1 (1991): 11-18. <http://eudml.org/doc/262426>.

@article{AndréBoivin1991,
abstract = {The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².},
author = {André Boivin, Roman Dwilewicz},
journal = {Annales Polonici Mathematici},
keywords = {holomorphic approximation; -function; tubular submanifolds},
language = {eng},
number = {1},
pages = {11-18},
title = {Holomorphic approximation of CR functions on tubular submanifolds of ℂ²},
url = {http://eudml.org/doc/262426},
volume = {55},
year = {1991},
}

TY - JOUR
AU - André Boivin
AU - Roman Dwilewicz
TI - Holomorphic approximation of CR functions on tubular submanifolds of ℂ²
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 11
EP - 18
AB - The purpose of this paper is to take a closer look at uniform semi-global (i.e. on compact subsets) holomorphic approximation of CR functions on tubular submanifolds in ℂ².
LA - eng
KW - holomorphic approximation; -function; tubular submanifolds
UR - http://eudml.org/doc/262426
ER -

References

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  1. [AH] A. Andreotii and C. D. Hill, E. E. Levi convexity and the Hans Lewy problem. Part I: Reduction to vanishing theorems, Ann. Scuola Norm. Sup. Pisa 26 (1972), 325-363. Zbl0256.32007
  2. [BT] M. S. Baouendi and F. Trèves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math. 113 (1981), 387-421. Zbl0491.35036
  3. [C] E. M. Chirka, personal communication. 
  4. [D] R. Dwilewicz, Holomorphic approximation in the theory of Cauchy-Riemann functions, in: Complex Analysis, Functional Analysis and Approximation Theory, North-Holland Math. Stud. 125, North-Holland, 1986, 71-82. 
  5. [DG] R. Dwilewicz and P. M. Gauthier, Global holomorphic approximations of CR functions on CR manifolds, Complex Variables 4 (1985), 377-391. Zbl0548.32011
  6. [DF] K. Diederich and J. E. Fornæss, Pseudoconvex domains: An example with nontrivial Nebenhülle, Math. Ann. 225 (1977), 275-292. Zbl0327.32008
  7. [FN] J. E. Fornæss and A. Nagel, The Mergelyan property for weakly pseudoconvex domains, Manuscripta Math. 22 (1977), 199-208. Zbl0391.32010
  8. [K] M. Kazlow, CR functions and tube manifolds, Trans. Amer. Math. Soc. 255 (1979), 153-171. Zbl0426.32005
  9. [M] A. I. Markushevich, Theory of Functions of a Complex Variable, Vol. III, Prentice-Hall, Englewood Cliffs, N.J., 1967. Zbl0148.05201
  10. [N1] J. Nunemacher, Approximation theory on totally real submanifolds, Math. Ann. 224 (1976), 129-141. Zbl0333.32015
  11. [N2] J. Nunemacher, Approximation theory on CR submanifolds, in: Proc. Sympos. Pure Math. 30, Part II, Amer. Math. Soc., 1977, 181-186. 
  12. [S] A. Sakai, Uniform approximation in several complex variables, Osaka J. Math. 15 (1978), 589-611. Zbl0409.32013

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